Mathematically Structured Programming Group
We also have a group photo from our away day to the Isle of Bute 2023.
Next MSP101 seminar
Approximation Theory for Distant Bang Calculus
Kostia Chardonnet (INRIA Nancy)
Tuesday 15 September 2026, 13:00, LT210
Abstract
Approximation semantics capture the observable behaviour of λ-terms. Böhm Trees and Taylor Expansion are their two central paradigms, related by the Commutation Theorem. While these notions are well understood in Call-by-Name (CbN), they have only recently been developed for Call-by-Value (CbV). However, these notions require a separate development for each evaluation strategy of the λ-calculus, which motivates the search for a unified approximation framework. The Bang-calculus provides such a framework: it subsumes both CbN and CbV through linear-logic translations and enjoys robust rewriting properties. We develop the approximation semantics of dBang (the Bang-calculus with explicit substitutions and distant reductions) by introducing approximation trees in the Böhm tradition together with Taylor expansion. We establish their fundamental properties, including a commutation theorem. Via translations, our results recover the CbN and CbV setting within a single unifying framework capturing infinitary and resource-sensitive semantics.See the MSP101 seminar page for a full list of future and past talks.
Research Themes
Our vision is to use mathematics to understand the nature of computation, and to turn that understanding into the next generation of programming languages.
We see the mathematical foundations of computation and programming as inextricably linked. We study one so as to develop the other. This reflects the symbiotic relationship between mathematics, programming, and the design of programming languages — any attempt to sever this connection will diminish each component.
To achieve these research goals we use ideas from the following disciplines:
- Functional Programming and Type Theory
- What does the future of programming languages look like? How does one take the logical structure of computation and turn it into a programming abstraction? Type theory allows us to do this by providing a language at an intermediate level of abstraction between a programming language and its logical foundations. Indeed, type theory could be said to be the ideas factory for programming languages.
- Logic
- Different logics are suitable for expressing and verifying different properties of programming languages or systems. We make use of a range of methods such as proof theory and coalgebra to understand the computational nature of proofs and systems intended to run without interruption. Those methods are driven by emerging problems in areas such as AI and security. We have particular strengths in modal logic, quantitative properties of systems, and logics for reasoning about concurrency.
- Category Theory
- How does one understand structure abstractly? How can one build theories that systematically build complex systems by composing descriptions of simpler ones? One uses category theory — that's how! Ideas such as monads and initial algebra semantics attest to the deep contribution that category theory has made to computation.